Question

A car moving with a speed of $50km/hr$ can be stopped by brakes after at least $6m$. If the same car is moving at a speed of $100km/hr$ the minimum stopping distance is :

• A. $12m$
• B. $24m$
• C. $6m$
• D. $18m$

Answer 1

The correct option is B

$24m$

Step 1: Given

Speed of the car,

$$\begin{gathered} u_1=50km/hr=\frac{250}{18}m/s \\ {u}_2=100km/hr=\frac{500}{18}m/s \end{gathered}$$

Stopping distance, $s_1=6m$

Final velocity, $v=0$

Step 2: Determine the acceleration of the car

Using the third equation of motion,

$$\begin{gathered} v^2={u_1}^2+2a{s}_1 \\ {0}^2={\left(\frac{250}{18}\right)}^2-2a\left(6\right) \\ a=16.07m/s^2 \end{gathered}$$

Step 3: Determine the minimum stopping distance for $100km/hr$

Using the third equation of motion again,

$$\begin{gathered} v^2={u_2}^2+2a{s}_2 \\ {0}^2={\left(\frac{500}{18}\right)}^2-2(16.07)\left(s_2\right) \\ {s}_2=24m \end{gathered}$$

Therefore, option B is the correct option.